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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 81 (page 757)

In Problems 75鈥� 82, algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 2 x - 3 y + z = 4 \\ - 3 x + 2 y - z = 17 \\ - 5 y + z = 6 \end{cases}$

Short Answer

Expert verified

The given equations $\{\begin{cases} 2 x - 3 y + z = 4 \\ - 3 x + 2 y - z = 17 \\ - 5 y + z = 6 \end{cases}$ has no solution.Hence the system is inconsistent

Step by step solution

01

Step 1. Given information

The given equations $\{\begin{cases} 2 x - 3 y + z = 4 \\ - 3 x + 2 y - z = 17 \\ - 5 y + z = 6 \end{cases}$

02

Step 2. Finding the values of x,y and z

Consider the equations $2 x - 3 y + z = 4, - 3 x + 2 y - z = 17$ and $- 5 y + z = 6$ .To solve these equations,it seems easiest to eliminate the variable z first.So,we add the first two equations

$2 x - 3 y + z = 4 + - 3 x + 2 y - z = 17 - x - y = 21$

$- x - y = 21 鈰� 鈰� 鈰� 鈰� (1)$

Again we add the last two equations

$- 3 x + 2 y - z = 17 + - 5 y + z = 6 - 3 x - 3 y = 23$

$- 3 x - 3 y = 23 鈰� 鈰� (2)$

Now we multiplay equation (1) by 3 and then substract equation (2) from it

$- 3 x - 3 y = 63 - 3 x - 3 y = 23 0 x + 0 y = 46$

$0 x + 0 y = 46 鈰� 鈰� 鈰� (3)$

Equation (3) has no solution.Hence the system is inconsistent

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Most popular questions from this chapter

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

$x^{2} + y^{2} = 8; x^{2} + y^{2} + 4 y = 0$

An area of $52 f e e t^{2}$ is to be enclosed by two squares whose sides are in the ratio of $2 : 3$ . Find the sides of the squares.

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\{\begin{matrix} 2 x + y = 1 \\ 4 x + 2 y = 3 \end{matrix}$

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

$x y = 4; x^{2} + y^{2} = 8$

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

$y = \sqrt{x}; y = 2 - x$

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